Question

The centrepetal force 'f' might depend on the mass, velocity of the body, and the radius of the path. if the value of constant k = 1, find a meaningful solution​

Answer 1

Answer:

F=rmv2 (where k=1)

Let F=k(m)x(v)y(r)z

Here, k is a dimensionless constant of proportionality. Writing the dimensions of RHS and LHS in Eq. (i), we have

[MLT2]=[M]x[LT−1]y[L]z=[MxLy+zT−y]

Equation the powers of M, L and T of both sides, we have,

x=1,y=2andy+z=1

or z=1−y=−1

Putting the values in Eq. (i), we get

F=kmv2r−1=krmv2

F=rmv2 (where k=1)